Tuesday, April 30, 2013

This game, “Chicken”, is similar
to Dilemma, except that the values of “lose” amd “draw” are interchanged. Now
draw is the worst outcome, and lose is the lesser evil. Unlike Dilemma, this
game has two Nash equilibria; win/lose and lose/win. This fact weakens
exploitation but strengthens intimidation.

This is the general Chicken
payoff matrix:

B

(A,B)|nicemean

|W=Win

----|--------|---------|T=Truce

nice|T,T|L,W|D=Draw

A-|--------|---------|L=Lose

mean|W,L|D,D|

-|--------|---------|where D<L<T<W

It is often presented as a war
game; Car Wars, involving irresponsible adolescents in high-powered vehicles.
In Car Wars Chicken, two cars approach each other in the same lane at high
velocity. The first driver to swerve out is not, as you might expect, lauded
for sanity, but jeered for lack of bravado. To “chicken out” is a loss in this
stupid game; to chicken others out is to win.

Chicken is a contest of
stubbornness, aggression, and intimidation. Like Dilemma, this game rewards
mutual cooperation, yet offers tempting opportunities for exploitation. In
Dilemma the dialog is between cooperation and competition; in Chicken the dialog
is between rationality and irrationality. There is little a loser can do ...
except threaten a draw, which is the worst outcome for both players. This is a
stubborn, unreasonable bargaining position; but that’s just what Chicken
favors.

Dilemma and Chicken both enforce
harmony via reciprocity, in the long run. Chicken’s long run is longer and
costlier; for Chicken is a metaphor for that most anti-social of games, War.

My father relates this anecdote
of wartime Chicken:

During the early 40’s he was trucking
high explosives for a certain Army project. It was a hazardous job, made more
hazardous by the presence of Chicken players on the road. Many times he found
some joker homing in on him; but my father assures me that he never paid the
slightest attention to such fools. He just kept on driving as if they weren’t
in his lane, and pretty soon they weren’t. That was my Dad!

Those guys didn’t have a chance.
After all, he was trucking those explosives for the Manhattan Project!

So my father said to me. From this
story I deduce (with horror and awe) that it’s a miracle that I even exist!

Monday, April 29, 2013

The Axelrod upper equilibrium
requires certain conditions. One of them is that the expected number of plays
be great enough; another is that the play not end at too definite at time. If
it does, then a “backwards induction paradox” destroys the Axelrod truce, no
matter how long the tournament.

Consider the following scene:

Curly is about to play with Moe
in a dilemma tournament sceduled to last exactly 100 rounds. Curly, a Silver
Rule player, is optimistic that he can convince Moe (an Iron Rule player) that
it’ll be in his own best interest to cooperate.

But Moe said, “What about the
100th round? Won’t that be the last one?”

Curly said, “Yes.”

“There won’t be any after the
100th?”

“Yes,” said Curly.

Moe asked, “So in the very last
play, what’s to keep me from defecting?”

“‘Cause I’ll defect the next...”
Curly said, then slapped himself on the face. “Alright, nothing will stop you
from defecting on the 100th play.”

“So you might as well defect too,
right?” Moe said, smiling.

“I guess so,” Curly said
reluctantly. “On the 100th play.”

Moe continued, “And what about
the 99th play? What’s to keep me from defecting then?”

“‘Cause I’ll defect the next...”
Curly said, then slapped himself on the face. “But I’ll defect on the 100th
play anyhow.”

“That’s right,” Moe said,
smiling.

“So nothing’s keeping you from
defecting on the 99th play.”

“That’s right,” Moe said,
smiling.

“So I should defect on the 99th
play also,” said Curly.

“That’s right,” Moe said. “Now,
what about the 98th play?”

And so they continued! Moe
whittled down Curly’s proposed truce, one play at a time, starting from the
end. By the time the conversation was over, Moe had convinced Curly that the
only logical course was for them to defect from each other 100 times, drawing
the tournament. And so they did; yet when Curly played with Larry (a Gold Rule
player) they cooperated 100 times, for a truce!

Thus we deduce, by mathematical
induction, that the prospect of abruptly terminated play, even if in the far
future, poisons the relationship at its inception. That is the “backwards
induction paradox”.

In dilemma play, cooperation requires
continuity to the end. Departure should not be at an expected time lest that
light the backwards-induction fuse; departure should be unannounced, at an
unexpected time.

We need an unexpected
departure; but this yields a paradox. Consider this following story about an
Unexpected Exam:

Once upon a time a professor told
his students, “Sometime next week I will give you an exam; and that exam will
be at an unexpected time. Right up until the moment I give you the exam, you
will have no way to deduce when it will happen, or even if it will happen. It
will be an Unexpected Exam.”

One of the professor’s students
objected, “But then the exam couldn’t happen on Friday; for by then it would be
expected!”

The professor said, “True.”

The student continued, “So
Friday’s ruled out.”

Another student said, “But if
Thursday’s the last possible day for an Unexpected Exam, then it’s ruled out
too; for by Thursday the Thursday exam will be expected!”

The professor said, “True.”

And so on; by such steps the
students concluded that the Unexpected Exam can’t happen on Friday, Thursday,
Wednesday, Tuesday, or Monday; so it can’t happen at all!

“So you don’t expect it?” said
the professor.

His students said, “No!”

The professor smiled...

The next Wednesday, he handed out
an exam, to the students’ surprise.

That’s the Paradox of the
Unexpected Exam. This also is a backwards induction paradox; but this time
it is a strangely false result rather than a strangely undesirable
result. This match suggests the following fable.

The same professor visited the
Dean; he said, “I will depart this school sometime during the next month. To
ensure cordial relations between us until that time, my departure will take
place on an unexpected day.”

The Dean retorted, “You couldn’t
leave on the 31st, for by then your Unexpected Departure would be expected.”

The professor agreed.

The Dean added, “Having ruled out
the 31st, the 30th is also ruled out; for it would be expected.”

The professor agreed to that too.

And so the conversation
continued; and in the end the Dean concluded, “Your Unexpected Departure can’t
happen on any day. Therefore I don’t expect it.” The professor agreed.

On the seventeenth day of the
month the professor departed, to the Dean’s astonishment.

This Paradox of the Unexpected
Departure is just what the doctor ordered; for here the failure of
backwards induction (so puzzling to the reason) is precisely what is needed to
defend the Axelrod equilibrium from its backwards induction proof!

Above I insisted that dilemma
tournaments use “open bounding”; that is, replay only if a random device
permits it. This ensures an Unexpected Departure; play will be finite, but
there will be no definite last play during which the Iron player is safe from
the danger of Silver retaliation.

The conclusion then is clear; let
none of your social relationships end too definitely; let there be some
possibility that you might encounter that person again, soon. (And conversely,
when you must leave, slip away quietly!)

Friday, April 26, 2013

The “Dilemma Wagers” chapter
shows how basic economic interactions involve dilemmas. This has profound
implications, both academic and political; for no existing economic ideology
has a rational dilemma strategy. All existing economic ideologies center upon
money; and money is the one Market element which is necessarily peripheral to
dilemma economics.

The Price Parley makes money part
of a dilemma wager; but though dilemma economics can involve money, it
cannot be based upon money. One cannot parley money for money; for the truce
in a money parley would mean an exchange of dollars; but my dollar is worth the
same as yours. This is the “fungibility of money”; by definition it precludes
mutual gain.

Money is inherently zero-sum, and
dilemma is inherently non-zero-sum; so money economics and dilemma economics
are mutually exclusive. Dilemma economics is Economics Without Money; a dilemma
with which many of us are all too familiar.

Neither Capitalism nor Socialism
can account for dilemma. Capitalism assumes, a priori, that any economic
interaction under capitalism is zero-sum by nature; this covers the win-lose
axis in dilemma. Socialism assumes, a priori, that any economic interaction
under socialism is zero-difference by nature; this covers the truce-draw axis
in dilemma. Thus both ideologies cover precisely one-half of the puzzle, and
between them lose sight of the real question.

Capitalism and Socialism
correspond, respectively, to the Iron and Gold rules. (Mixed Government tends
to resemble the Random strategy.) The Gold rule would truce with itself; but it
is vulnerable to invasion and defeat by the Iron rule; and the former strategy
draws against itself. Thus Capitalism describes a world that should not endure;
and Socialism describes a world that cannot endure. Neither one is the world
which does endure; for both strategies are dead! What endures is what lives,
and is thus a conundrum, a mystery, a dilemma.

We should accept such dilemmas,
even embrace them; for dilemma makes free-enterprise democracy possible. If
there is to be free enterprise, then there must be profit; but if there is to
be democracy, then that profit must go to the people. Therefore democratic
free-enterprise requires mutual profit; where the people profit from each
other!

Mutual profit is, by definition,
non-zero-sum. It implies the possibility of mutual loss, along with the
win/loss struggle of Capitalist competition; thus full dilemma emerges.

Mutual profit is the Market’s
truce. It is economic peace, attained via justice tempered by mercy. Mutual
profit flourishes best in communities of mutual aid. It lives by the Silver
Rule; value for value.

Mutual profit transcends both
Capitalism and Socialism; the first because it is mutual, the second because it
is profit. Mutual profit creates social order spontaneously, without coercion;
therefore mutual profit is inherently Anarchist. Mutual profit subverts the
State.

Thursday, April 25, 2013

This paradox is a failed attempt
to resolve Dilemma. It teaches us that not even a confrontation with a Superior
Being can make certain people behave themselves.

In the Predictor’s Paradox, you
(an ordinary mortal) are shown a pair of boxes. Box A is open; $1 can be seen
within. Box B is shut; it contains either $100 or $0. The other player claims
to be a Superior Being who can predict your actions. “If you choose to take
both boxes”, says the Being, “then you’ll discover that I’ve punished you by
putting nothing in box B; but if you have faith in me and take only box B, then
you’ll find my reward of $100 there.”

Let us assume that previous
experience has shown that the Being can apparently make good on its claim of
being able to predict your actions; what should you do? Here’s the game matrix:

payoff for mortal

Being

|rewardspunishes

----|----------|-----------|

takes
box B |100|0|

mortal-|----------|-----------|

takes
both|101|1|

-|----------|-----------|

Meanwhile, what’s in it for the
Being? Let us suppose, for the sake of symmetry, that the Being’s game matrix
is as follows:

payoff
for Being

Being

|rewardspunishes

----|----------|-----------|

takes
box B |100|101|

mortal-|----------|-----------|

takes
both|0|1|

-|----------|-----------|

Presumably the Being values your
faith one hundred times more than the material profit of punishing you. This
way you and the Being are in a Dilemma game, where win = 101, truce = 100, draw
= 1 and lose = 0.

Your best move depends on how
well the Superior Being can foretell your actions. If the Being can correctly
predict your actions with probability exceeding (in this case) 50.5 %, then the
expected value of taking one box exceeds that of taking both. In this case,
reasoning by expected value favors leaving the $1 alone; yet taking the $1
would still be a dominant strategy!

Two different lines of argument
yield two opposite recommendations. How are we to decide? That is the question.
The Predictor’s Paradox represents a dispute between the principles of Dominance
and Expectation. It shows that not even a confrontation with a Superior Being
can make Iron-rule players behave themselves! That $1 sitting there, just
begging to be taken... how can they resist such a devilish temptation? If therereally were a Superior Being, then this
little test would ensure the self-defeat of all habitual exploiters, whilst
humbler folk win riches!

Actually I’m satisfied neither
with blind faith, nor with exploitation. Blind faith in the Being is a Gold Rule
strategy, and as such is vulnerable if the Being is an Iron Rule player.
Similarly the attempt to exploit the Being is an Iron Rule strategy. The
optimum long run strategy is the Silver Rule:

Do Unto Others As They Have Done
Unto You.

This principle of cosmic justice
is so powerful that even a Superior Being must meet us there on equal terms.

Therefore, if I were ever to
confront a Superior Being in this fashion, I would form the intention to take
either $1 or $100, but not $0 nor $101. After all, why should I ignore the $1
bill if I get nothing otherwise? And conversely, why should I try to cheat a
Superior Being of $1 if it already gave me $100?

Thus I, a mere mortal ruled by
greed and fear, propose to make myself the equal of a Superior Being! I leave
it to you, dear reader, to judge the soundness of my thinking; but note that
within this mental context, the Being has every reason to give me $100.

Some may object that there are no
Superior Beings in evidence with whom to play this game; to this I reply that
the Silver Rule is so powerful that it enables a mere mortal to make a passable
imitation of a Superior Being, provided that the shadow of the future is long
enough.

For let us iterate this game with
open bounds, with replay probability 99/100, so the expected number of plays is
100. Rescale the payoffs accordingly, at 1/100th of the payoffs noted above;
i.e. 1 cent in box A, $0 or $1 in box B. In
this Predictor’s Tournament, I shall play the Superior Being’s role; my
strategy will be tit-for-tat. If you take both boxes on a given round, then on
the next round I’ll leave box B empty; and if you take only box B, then on the
next round I’ll put $1 in box B. (In a sense, the Superior Being that I emulate
is Reciprocity itself!)

If you are rational, and if play
is long enough, then we will attain truce; you will always take only box B, and
you will always find $1 in it. Though I can’t predict you, I do remember you;
so in the long run it will be in your interest to act as if I could
predict you. Continuity is the key; if the “shadow of the future” is long
enough, then my memory, like the Superior Being’s prophesy, will enforce social
harmony. My hindsight equals Reciprocity’s foresight.

A shadow is haunting Earth; the
shadow of the future. Will we be or will we not be? That is the question. When
the future’s shadow is short, not even a Superior Being can deter the wicked
from maximizing profit; but when the shadow of the future extends, then you and
I can be like unto Superior Beings, and peace breaks out! Blessed be the shadow
of the future!